 Welcome back we are now going to look at the equation of state of an ideal gas. The phrase equation of state will occur so often in thermodynamics that we will frequently use the short form EOS for it. We have defined the Kelvin scale of temperature as T by T at the triple point of water Pv divided by Pv at the triple point. Now for this scheme to work as a ideal gas Kelvin thermometer we have to use an ideal gas as a working fluid. Now let us say that we are looking at this behavior as specified by the ideal gas and that itself gives us the equation of state of an ideal gas. Let me put Pv on the left hand side and push everything on the right hand side and you will get this simple relation where all terms containing Tp as the subscript I have combined together. Actually this is the basic equation of state of an ideal gas. Now you will notice that there is one parameter here and P and T are intensive properties but the volume is an extensive property. So this parameter will depend on the mass of the system or the actual volume of the system. So what we do is we write this in terms of specific mass, mass per unit volume. So we write this as m into Pv by T at the triple point of water of that ideal gas multiplied by T. Now this term which is the ratio of the product of Pv to T at the triple point of water of that ideal gas which we are looking at is given the symbol R and this R is known as the gas constant for that particular gas. If we approximate oxygen as an ideal gas we will have one value of the gas constant that could be the gas constant for oxygen. If we use nitrogen and consider it to be an ideal gas we will have a different gas constant for nitrogen. Similarly any gas when approximated as an ideal gas will have a value of R which is specific to that gas. So we should remember that the equation of state of an ideal gas can be written down either as Pv equals mRT or if we divide throughout by m then on the left hand side we will get V by m and that can be written as the specific volume. So you will end up with Pv equals RT where R is the gas constant for that particular gas and let us look at the units of R. Notice that units of R will be units of ratio of product of pressure and specific volume to temperature. Since Pv the product has units of work done say joule T will have to have units of Kelvin ideal gas temperature so unit is Kelvin. So the unit of this will be joule T per kilogram Kelvin. Kilogram comes in because this is specific volume or it could be kilo joule per kilogram Kelvin. Now let us visit physical chemistry. We know that the amount of matter can either be represented by mass say m in kilograms or it can also be represented in terms of moles say m1 kilo mole of any given substance contains exactly the same number of atoms or molecules as appropriate the Avogadro number and the conversion factor between this is n in kilo mole is mass in kilogram divided by the molecular weight which is kg per kilo mole m here is what is generally known as the molecular weight or molecular mass the unit kg per kilo mole. The advantage of this is in our equation of state for an ideal gas we may wish to use moles instead of mass and if you do that you will get a modified form of the ideal gas equation of state where R u is the universal gas constant. So remember that in the first right hand side of the equation m is mass R is the gas constant for that given gas and T is temperature mass as the unit kg the gas constant as the units say kilo joule per kilo gram Kelvin or joule per kilo gram Kelvin and temperature as the unit on the second right hand side n is the number of moles unit will be kilo mole universal gas constant will have units of joule per kilo mole Kelvin or kilo joule per kilo mole Kelvin and of course T will have the units of Kelvin being temperature. The advantage of this is this number the universal gas constant is independent of the identity of the gas and the value is 8.314 kilo joule per kilo mole Kelvin thank you.